We consider the renormalization of strong-coupling expansions for the Green's functions of a quantum field theory. For the $g_0{\phi }^4$ theory that is an expansion in powers of ${g_0}^{-\frac{1}{2}}$. In less than three space-time dimensions, we find that conventional renormalization, that is mass, coupling-constant, and wave-function renormalization, does not lead to a divergence-free renormalized strong-coupling expansion. In three or more space-time dimensions there is a renormalized strong-coupling expansion which is finite term by term, but the resultant renormalized Green's functions are trivial.

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